On topological spaces of orders

摘要

We study the space of linear orders on a given set X, denoted by O_p(X), endowed with the topology of pointwise convergence. We show, in particular, that if |X| = ω_1 or |X| = ω_0 then O_p(X) is homeomorphic to 2~(ω_1) and 2~(ω_0), respectively.